Work and pensions secretary Iain Duncan Smith dismissed an offer from the equality watchdog to help MPs and peers understand the true impact on disabled people and other groups of his new welfare bill.

Letters between the Equality and Human Rights Commission (EHRC) and Duncan Smith (pictured) were published this week on the commission’s website, following a freedom of information request.

In her letter sent in September, Rebecca Hilsenrath, EHRC’s interim chief executive, had asked Duncan Smith “what your thoughts are on ensuring that the impact assessments are sufficient to address these issues and support the proper scrutiny of the bill”.

In his response last month, Duncan Smith ignored her offer of assistance and told her that the impact assessments already use “the most robust analysis available to give a good assessment of both the rationale for and the impacts of the reforms” in the bill.

In a briefing on its website, EHRC says it is concerned that parts of the welfare reform and work bill “could exacerbate, rather than reduce, existing inequalities”.

It says it is concerned that the impact assessments and human rights memorandum which accompany the bill “do not fully assess the effect of the bill on equality and human rights”, which “may make it difficult for parliamentarians to properly consider the implications of the measures in the bill”.

The watchdog also says the government should review welfare reform measures in the bill – including the proposed reduction of the benefit cap, the freeze on many benefit rates, and the WRAG cut – so it can assess how they comply with the government’s international human rights obligations, including the UN Convention on the Rights of Persons with Disabilities.

An EHRC spokesman said: “We continue to raise our concerns and make representations on this issue.

“For example, at Commons report stage we urged MPs to support an amendment which would have prevented implementation of the bill until an assessment of the cumulative impact and impact on equality of reforms to tax credits and benefits announced in the 2015 summer budget is presented to both Houses of Parliament.

“This makes clear that the commission is concerned that the impact assessments and human rights memorandum which accompany the bill do not fully assess the effect of the bill on equality and human rights.”

The letters were published as the bill began its progress through the House of Lords, with one Tory peer saying she was appalled by the wording of the government’s impact assessment of its proposed cut of £29 a week for future claimants placed in the work-related activity group (WRAG) of employment and support allowance.

The assessment says the cut would “remove the financial incentives that could otherwise discourage claimants from taking steps back to work”.

Baroness Browning, who has a son with autism, told the welfare reform minister Lord Freud: “I am disgusted with those words.”

Despite her comments, Lord Freud spoke in the debate of the “perverse incentives” of paying disabled people in the WRAG more than people on the mainstream jobseeker’s allowance.

The disabled peers Lord [Colin] Low and Baroness [Tanni] Grey-Thompson, along with their fellow crossbench peer Baroness Meacher, are heading a parliamentary review into how the proposed WRAG cut might affect disabled people.

Lord Low dismissed the bill as “another round of ideologically-driven cuts to welfare”, and told fellow peers that the government’s target of cutting another £12 billion from benefits spending “cannot but have a devastating impact on poor people who depend on benefits”.

Baroness Grey-Thompson suggested that the WRAG cut could move disabled people further from the workplace, by creating an incentive for them to be placed in the ESA support group, where there would be limited employment support available to them.

She added: “I struggle to see how cutting support could incentivise disabled people into work, and I am looking forward to the DWP’s convincing arguments in this area.”

In response to criticisms of the WRAG cut, Lord Freud quoted a 10-year-old report by the OECD which said that “financial incentives to work can be improved by either cutting welfare benefit levels, or introducing in-work benefits while leaving benefit levels unchanged”, although it was not clear whether this referred to disabled benefit claimants.

He added: “This change, combined with the new funding [the government plans to spend an extra £100 million a year of the £640 million savings from the WRAG cut on improving employment support for disabled people]is about providing the right incentives and support to encourage more people to move closer to the labour market.”